High-Performance γ-Al2O3 Multichannel Tube-Type Tight Ultrafiltration Membrane Using a Modified Sol-Gel Method

We introduced a modified sol-gel method using polyvinyl alcohol (PVA) as an additive to improve the permeability of γ-Al2O3 membranes by minimizing the thickness of the selective layer and maximizing the porosity. First, the analysis revealed that the thickness of γ-Al2O3 decreased as the concentration of PVA increased in the boehmite sol. Second, the properties of the γ-Al2O3 mesoporous membranes were greatly influenced by the modified route (method B) compared to the conventional route (method A). The results showed that the porosity and surface area of the γ-Al2O3 membrane increased, and the tortuosity decreased considerably using method B. This effect was attributed to the adsorption of PVA molecules on the surface of the boehmite particles, which depended on the synthesis route. The experimentally determined pure water permeability trend and the Hagen–Poiseuille mathematical model confirmed that the modified method improved the performance of the γ-Al2O3 membrane. Finally, the γ-Al2O3 membrane fabricated via a modified sol-gel method with a pore size of 2.7 nm (MWCO = 5300 Da) exhibited a pure water permeability of over 18 LMH/bar, which is three times higher than that of the γ-Al2O3 membrane prepared using the conventional method.


Introduction
Recently, the demand for resource recovery from harsh industrial wastewater has increased due to resource depletion and the need to achieve net-zero carbon emissions. In this regard, ultrafiltration (UF) membranes have been widely studied and utilized in various fields, including the recovery of dyes from industrial wastewater, cooling water for turbines, and the pretreatment for reverse osmosis. The molecular weight cut-off (MWCO) of tight UF membranes is 1000-10,000 Dalton (Da) [1]. Ceramic UF membranes with high tunability, stability in harsh chemical environments over a wide temperature range, and resistance to organic matter [2,3], are considered to have the most potential for wastewater treatment. Alumina (Al 2 O 3 ) is a widely used ceramic material for membrane applications owing to its advantages such as high-temperature filtration [4] and hydrophilic nature, which mitigates fouling [5].
The most efficient routes for ceramic fabrication include sol-gel, dip-coating, and sintering [6]. The sol-gel process is considered to be the primary technique for fabricating ceramic mesoporous membranes. Colloidal sols consist mainly of precursors, hydrolysis agents, and additives, including peptizing agents and organic polymers [7][8][9].
Mesoporous γ-Al 2 O 3 membranes were the first, and are currently the most widely investigated membranes for UF applications [10]. Mesoporous γ-Al 2 O 3 membranes with an average pore size of 3-5 nm have been reported in the literature [11][12][13][14][15] as presented in Table 1, and they have been used as an intermediate layer for top nanofiltration coatings [16]. Nanofiltration γ-Al 2 O 3 membranes with a mean pore size of 1-2 nm have also been developed [17,18]. However, the permeability of these membranes is not sufficient for industrial applications. The pure water permeability is generally reported to be less than 10 LMH/bar. One effective approach to fabricating γ-Al 2 O 3 membranes with high permeability is to modify their morphological characteristics, including the surface area and porosity. These characteristics mainly depend on the synthesis conditions and the incorporation of additives [19][20][21]. In our previous research [22], we investigated the effect of acetic acid as a peptizing agent on the formation of mesoporous α-Al 2 O 3 membranes. We optimized the peptization step to produce boehmite sol with a smaller particle size, which mitigated the growth of particles during the transformation from the γto the α-phase. The α-Al 2 O 3 membrane with the smallest mean pore size of 12.5 nm (MWCO = 163 kDa) was obtained by synthesizing boehmite sol at pH 3.5 with a 24 h peptization time.
In this study, we investigated the effect of organic additives on the characteristics of γ-Al 2 O 3 membranes. To date, organic polymers, including polyvinyl alcohol (PVA), cellulosic compounds, and polyglycols, have been added as binders in boehmite sol to prevent crack generation during thermal treatment [23]. However, the effect of organic additives on the morphological properties of membranes synthesized using boehmite sol remains unclear.
PVA is the most frequently used additive for fabricating defect-free and stable Al 2 O 3 membranes [24,25]. In the conventional sol-gel method, PVA is added to the sol after peptization. In this study, we introduce a modified sol-gel method using PVA to improve the permeability of a γ-Al 2 O 3 tight UF membrane by minimizing the thickness of the selective layer and maximizing porosity. Research has been conducted on the development of unsupported Al 2 O 3 membranes by altering the order in which PVA is added during the sol-gel process [26]. However, the effect of the interaction between boehmite particles and PVA molecules on the filtration properties has not been fully investigated. Therefore, further research into the synthesis of γ-Al 2 O 3 membranes focusing on the interaction with PVA is required.
This study aimed to investigate the effect of PVA addition on the properties of γ-Al 2 O 3 membranes. Emphasis was placed on the comparison of the membrane morphology and permeability before and after the peptization step as a function of the amount of PVA added.

Synthesis of Boehmite Sol
The synthesis of the boehmite sol involved several steps. Aluminum tri-sec-butoxide (ASB, 97%, Sigma-Aldrich, Darmstadt, Germany) was used as the precursor. Ethyl alcohol (C 2 H 6 O, 99.9%, Samchun Chemicals, Seoul, South Korea) was used as a solvent, deionized (DI) water as a hydrolysis agent, and acetic acid (CH 3 CO 2 H, ≥99.7%, Sigma Aldrich, Darmstadt, Germany) as a peptizing agent. The sol was maintained at pH 3.5 with subsequent stirring for 24 h. The sol-gel reaction of the boehmite showed hydrolysis and pol condensation, shown in Figure S1. The detailed procedure was described in our previous study [22]. A 10 wt.% aqueous solution of PVA (M.W. 31,000-50,000, Sigma Aldrich, Darmstadt, Germany) was prepared in DI water. This PVA solution was incorporated into the boehmite sol using two different approaches. In the conventional approach (method A), the PVA was introduced into the boehmite sol after peptization, whereas in the modified approach (method B) it was added before peptization, as shown in Figure 1. The final membrane layers synthesized by methods A and B are denoted as membranes A and B, respectively. A γ-Al 2 O 3 membrane without the PVA additive was also prepared as a reference (membrane S). The substrate material used for the preliminary experiments was a disk-shaped α-Al 2 O 3 porous support with a diameter of 47 mm. In the final stage, a multi-channel α-Al 2 O 3 porous support with cylindrical tube-shaped dimensions (outer diameter: 24 mm, length: 150 mm) and 30 inner holes (inner diameter: 2 mm) prepared in our laboratory was used for the synthesis of the active γ-Al 2 O 3 membrane layer [27]. The average pore size of macroporous support and top microfiltration layer was reported to be 0.8 µm and 0.07 µm, respectively. γ-Al 2 O 3 membranes were formed on the inner channels of the tubular substrate by dip-coating with a soaking time of 50 s. Finally, the coated substrates were dried at ambient temperature for 24 h and sintered at 600 • C (1 • C/min) for 3 h.

Characterization
A low-voltage scanning electron microscope (Merlin Compact, Carl Zeiss, Jena, Germany) was used to observe the microstructure of the membrane and the thickness of the coatings. A ViscoQC™ 100-L viscometer (Anton Paar, Graz, Austria) was used to measure the viscosity of the boehmite sol. The specific surface area and pore size of the unsupported membranes were measured using the BET method and a surface area and porosity analyzer (BELSORP-mini II, MicrotracBEL, Osaka, Japan). The membrane porosity was determined using the gravimetric method [28]. Membranes were immersed in hot water for 3 h before measuring their wet weight (m 2 ). The dry weight (m 1 ) of the membranes was measured by placing them in an oven for 24 h. The membrane porosity (ε) was calculated using Equation (1): where ρ 1 and ρ 2 are the densities of Al 2 O 3 (3.95 g/cm 3 ) and water (1 g/cm 3 ), respectively. The filtration performance of the γ-Al 2 O 3 membranes was determined by measuring the pure water (PW) permeability using a dead-end filtration system. The measurements were carried out at a transmembrane pressure of 2 bar, and the permeability was reported in units of LMH/bar (L·m −2 ·h −1 ·bar −1 ). The MWCO values were determined employing polyethylene glycol (PEG, Sigma-Aldrich, St. Louis, MO, U.S.A) retention experiments at six different molecular weights (1000, 1500, 3000, 6000, 10,000, and 20,000 g/mol) using a total organic carbon (TOC) analyzer (TOC-V CPH, Shimadzu Corp., Kyoto, Japan). The molecular mass of PEG corresponding to 90% retention was determined as the MWCO of the membrane. Additionally, regression analysis was performed using the extreme model to study the relationship between the rejection coefficient and the solute diameter [29].  Gu et al. [30] described the formation of a membrane layer on a porous substrate using a mathematical model. The detailed parameters of the model can be found in equation (S1).

Effect of PVA Addition on the Thickness of γ-Al 2 O 3 Membranes
According to the proposed model, when the same substrate and dip coating conditions are used, the thickness of the membrane is directly proportional to the surface tension and inversely related to the viscosity of the suspension. To demonstrate the proposed decrease in the membrane thickness with increasing PVA concentration, the model must be validated.
To this end, a boehmite sol was prepared with increasing PVA concentration ranging from 0 wt.% to 55 wt.%. The viscosity of the sol was determined by using a viscometer. The thickness of the top membrane layer was monitored using scanning electron microscopy (SEM). The effect of the sol viscosity on the thickness of the γ-Al 2 O 3 membrane is illustrated in Figure 3. The viscosity of the solution increased with PVA concentration, whereas the thickness of the membrane layer on the α-Al 2 O 3 substrate surface decreased. Moreover, the addition of PVA decreased the surface tension of the solution [31][32][33]. Consequently, adding PVA to the boehmite sol likely reduced the surface tension of the boehmite chains. According to the model, the membrane thickness tends to decrease with increasing viscosity and decreasing surface tension. Therefore, these results support the presented model and explain the decreasing trend of the membrane thickness as a function of the increasing PVA concentration in the boehmite sol. Generally, the coating layer thickness should be as small as possible without any defects to obtain higher permeate flux [30]. As shown in Figure 3, the minimum thickness of the γ-Al 2 O 3 membranes occurred at a PVA concentration of 50 wt.%. There was no significant improvement in membrane thickness with higher PVA concentrations. Additionally, the surface area of the membrane increased with the increasing concentration of PVA, as shown in Figure S2. Both minimum thickness and greater surface area favored the optimization of PVA at a concentration of 50 wt.% for further investigation.

Influence of the Fabrication Routes on the Properties of γ-Al 2 O 3 Membranes
In the previous section, we discussed the effect of PVA addition on the thickness of γ-Al 2 O 3 membranes. In this section, we investigate the influence of the fabrication route on the properties of the γ-Al 2 O 3 membranes. Figure 4 shows the SEM micrographs of the top surface of the membranes prepared with and without PVA addition. Crack-free membranes with homogenous surface morphologies were obtained. Nitrogen adsorption experiments were conducted to determine the pore characteristics of the prepared γ-Al 2 O 3 membranes. The quantitative nitrogen sorption data are reported in Table 2. Membrane S exhibited the smallest surface area and pore volume. On the other hand, membranes A and B demonstrated different pore characteristics, despite the similar PVA content. Furthermore, membrane B exhibited the highest surface area and pore volume. However, the average pore size of membrane B was approximately 7.4 nm, which was slightly larger than that of membrane A (7.0 nm). The addition of PVA increased the porosity of the γ-Al 2 O 3 membrane (membrane S → membrane A), as shown in Table 3. Modifying the sequence of PVA addition resulted in a further increase in porosity, from 37.3 to 40.8% (membrane A → membrane B). Table 3. The values of porosity of γ-Al 2 O 3 membranes: membrane S (without the addition of PVA); membrane A (addition of PVA after peptization); and membrane B (addition of PVA before peptization). It is evident from the data that incorporating PVA before the peptization reaction significantly improves the morphological properties of the γ-Al 2 O 3 membranes during sol-gel synthesis. The effect of the modified sol-gel method B on the surface area and porosity can be explained by examining the interaction mechanism between the PVA and the boehmite sol.

Membrane
First, it is important to consider the chemical nature of PVA. PVA contains a large number of intermolecular and intramolecular hydrogen bonds. When it is added to a suspension, it forms a hydrogen bond with the hydroxyl groups on the surface of the boehmite particles [34,35]. Moreover, commercial PVA is not completely hydrolyzed and contains charged groups. PVA (hydrolysis degree 98%) contains 2% of unhydrolyzed chains of acetate groups (CH 3 COO -) [36]. These negatively charged groups allow PVA to interact electrostatically with the solid particles. Thus, the adsorption of PVA on the surface of the boehmite particles is governed by both hydrogen bonding and electrostatic forces. The proposed interaction of PVA during the synthesis of γ-Al 2 O 3 membranes using methods A and B is illustrated in Figure 5.
The initial step of method A involved adding acetic acid as a peptizing agent after the hydrolysis reaction, resulting in the synthesis of membrane S. The pH of the hydrolyzed sol was in the range of 8.0-9.0, but it decreased with higher acetic acid concentrations. The boehmite sol was optimized at a pH of 3.5, which was much lower than the isoelectric point (pH 7.2-8.2) [37]. As previously reported [22], acetic acid dissociates into anions (CH 3 COO − ) and cations (H + ) that adsorb on the surface of boehmite particles. As a result, electrostatic repulsive forces are generated among the particles that stabilize the colloidal suspension and form a defect-free membrane. In the following step, we introduced PVA as an organic additive in the peptized boehmite sol for the preparation of membrane A. As previously discussed, PVA interacts with boehmite particles via hydrogen bonding and electrostatic interactions. However, the presence of acetic acid ions on the surface of boehmite particles inhibits the reaction and adsorption of PVA molecules. As a result, a thin PVA layer adsorbed on the surface of the boehmite particles. As the amount of adsorbed PVA decreases, its pore-forming effect is compromised. The BET results support the proposed effects, demonstrating that the pore size of membrane A was smaller with a lower surface area compared to membrane B. This indicates that adding PVA does not significantly improve the morphological properties of the synthesized membrane using method A.
In the modified method B, PVA was introduced as an organic additive prior to the peptization reaction. This allowed PVA to interact with boehmite particles without the interference of acetic acid. It is expected that a larger number of PVA molecules can be adsorbed on the solid surface, leading to the enhancement of the pore-forming effect during the calcination process. This explains the slightly larger pore size of the modified γ-Al 2 O 3 membrane, and the higher surface area and porosity compared to the conventional membrane A.
The structural differences between membranes A and B also affect their tortuosity. The tortuosity (τ) depends on porosity, particle shape and connectivity. Figure 6 shows the effect of tortuosity according to the pore characteristics of the sintered membranes A and B. Since the porosity of membrane B is higher than that of membrane A, membrane B has a lower tortuosity. Many attempts have been made to derive a correlation between tortuosity and porosity by introducing parameters representing the membrane pore structure [38]. The tortuosity has been reported to be inversely proportional to the porosity. As the porosity increases, the tortuosity decreases and converges to the ideal value of 1. Representative correlations between the tortuosity and the porosity are as follows [39]: Equations (2) and (3) were derived from the geometry of interstices between closed packed spheres and loose packed spheres, respectively. According to Darcy's law [40], high porosity and surface area, and low tortuosity contribute to the synthesis of γ-Al 2 O 3 membranes with a high PW flux. This can be validated by experimentally determining the permeate flux of the membrane and comparing it to the mathematical model, as described in the next section. Figure 7 shows the PEG retention curves for the γ-Al 2 O 3 membranes. The MWCO of membranes A and B were 3700 Da and 5300 Da, respectively. The corresponding Stokes diameter of the PEG molecules was calculated using Formula (4) [41].

Performance of the γ-Al 2 O 3 Membranes
Membrane A exhibited a pore diameter of 2.38 nm, while the calculated pore diameter of membrane B was 2.78 nm. Based on these results, both γ-Al 2 O 3 membranes can be characterized as tight UF membranes with pore sizes in the mesoporous range. The difference in pore size between the membranes is attributed to the proposed effect of PVA adsorption on the surface of the boehmite particles. A PW permeability test was performed using a dead-end filtration system. The permeability curves are presented in Figure 8. Membrane S exhibited the lowest permeability among the membranes. The PW permeability increased from 2.4 LMH/bar to 6.1 LMH/bar, with the addition of PVA during the synthesis of boehmite sol. The permeability of membrane B was 18.2 LMH/bar, which is three times higher than that of membrane A (6.1 LMH/bar). The variation of PW permeability was in agreement with the results of the porosity and surface area. A comparison of membranes A and B showed that the former had a relatively smaller surface area and porosity than the latter, and the latter had a higher permeability than the former. This indicates that the permeate flux increased with the porosity and surface area.
The effects of membrane thickness, pore size, and porosity on the permeate flux can be validated by the Hagen-Poiseuille model. The model was described in detail by Equation (S2) [42].
As per the model, the membrane thickness, pore size, and porosity play a significant role in the calculation of permeate flux. The thickness of the membrane can be minimized using PVA as a binder. The permeability of membranes A and B was significantly higher than that of membrane S. In addition, membrane B exhibited higher permeability because of its larger pore size and porosity compared to membrane A.
We also compared our results with those of γ-Al 2 O 3 membranes reported in the literature ( Table 1). The γ-Al 2 O 3 membrane synthesized by the modified method B in this work exhibits a much higher pure water permeability than the γ-Al 2 O 3 membranes prepared by the conventional method in the literature.  Figure 9 shows the correlation between MWCO values and the PW permeability of γ-Al 2 O 3 ultrafiltration (UF) membranes reported in the literature [11,12,16,20,43,44]. It is evident that membrane thickness, porosity, and surface area play important roles in determining the permeate flux. Following the high filtration efficiency of γ-Al 2 O 3 membranes synthesized using the modified method B, we successfully developed it on a multichannel cylindrical tube-type support. Figure 10 shows a well-integrated active membrane layer with uniform thickness along the substrate. The thickness of the γ-Al 2 O 3 membrane coated on a multichannel cylindrical tube-type substrate was in accordance with the membrane thickness observed for a disk-type substrate. This demonstrates the potential of the modified γ-Al 2 O 3 membrane for industrial applications with high performance.

Conclusions
The mesoporous γ-Al 2 O 3 membrane was successfully prepared through a modified sol-gel route followed by a dip coating and sintering process. The properties of γ-Al 2 O 3 membranes, with different concentrations of PVA from 0 to 50 wt.% and by changing the fabrication route, were investigated in detail.
The membrane optimized at a PVA concentration of 50 wt.% exhibited a minimum thickness of approximately 1.8 µm. The SEM micrographs revealed that the γ-Al 2 O 3 membrane with PVA concentration of 50 wt.% exhibited minimum thickness. There was no difference in membrane thickness by increasing PVA concentration above 50 wt.%. The BET specific surface area also increased with increasing concentration of PVA.
Two sol-gel methods, referred to as methods A and B, were used to synthesize γ-Al 2 O 3 membranes with optimized concentration of PVA. Method A is the conventional method of adding PVA after peptization, while method B is a modified route in which the order of PVA addition is altered. The analysis indicates that adding PVA before peptization during the modified method B leads to an increase in the porosity and surface area, and a decrease in tortuosity. This can be explained by the interaction between PVA macromolecules and boehmite particles without the interference of acetic acid ions, which enhanced the adsorption of PVA on the surface of the boehmite particles. The high adsorption facilitated the pore-forming effect of PVA.
Finally, a γ-Al 2 O 3 membrane with a high pure water permeability of 18.2 LMH/bar was obtained using a modified sol-gel method. The addition of PVA in a modified synthesis approach proved to be effective in tuning the membrane morphological properties and increasing the PW permeability.